X-Message-Number: 4349
Newsgroups: sci.cryonics
From:  (Marvin Minsky)
Subject: Re: " Neural nets
Message-ID: <>
References: <3o4sb5$>
Date: Wed, 3 May 1995 01:47:51 GMT

In article <3o4sb5$>  writes:
>    ---- CryoNet Message Auto-Forwarded by <> ----
>
>From: 
>Date: Mon, 1 May 1995 15:51:34 -0700
>Subject: "SCI.CRYONICS" Neural nets
>
>At least four contribotors to CryoNet (Keith F. Lynch, John 
>Clark, Eugen Leitl, and Paul Wakfer) have made the claim that 
>neural nets are computationally universal, i.e. that any 
>recursive function can be computed by a suitable neural net.  I 
>have asked to see a cite to the literature that demonstrates this 
>claim; no-one has supplied one yet. I believe that is because the 
>claim is FALSE.
>
>The concept of neural net traces back to the original paper of 
>McCulloch and Pitts [1].  The logician Stephen Cole Kleene 
>abstracted from their ideas the notion of a finite automaton, and 
>proceeded to describe exactly what sets of inputs were accepted 
>by such automata:  they are just the regular sets of strings over 
>the input alphabet.  Finite automata are far weaker than Turing 
>machines, because they do not have any scratch memory (like the 
>infinite tape on a Turing machine). The class of regular sets is 
>much simpler than the class of recursively enumerable sets 
>accepted by Turing machines.

This is technically correct but 'spiritually' misleading.  There do
not exist any "Turing machines" in the sense you're describing, simply
because there are no infinite tapes. Furthermore, it is easy to design a
neural net that is divided into a fixed, finite-state machine and a
general tape-like memory.  Then the net will behave just like a
Universal Turing machine until the memmory is used up.

Human brains have never been shown to be able to store more than the
order of 1 but per second in memory, over extended periods--and
there's no evidence that a human brain can run out of memory in a
normal lifetime.

Consequently, the argument that nets are not universal appears to be a
misleading and, perhaps, cantankerous complaint.  Although true, it is
only so in a trivial sense, useful only for misleading novices.


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